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The Plans Theorem for Cones over Generalized -Graphs. / Mednykh, I. A.
в: Siberian Mathematical Journal, Том 67, № 1, 01.2026, стр. 99-109.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The Plans Theorem for Cones over Generalized -Graphs
AU - Mednykh, I. A.
N1 - Mednykh, I.A. The Plans Theorem for Cones over Generalized I-Graphs. Sib Math J 67, 99–109 (2026). https://doi.org/10.1134/S0037446626010106 The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2026–0026).
PY - 2026/1
Y1 - 2026/1
N2 - We consider a family of graphs generalizing the family of -graphs, which in turn includes generalized Petersen graphs and prismatic graphs.The paper is devoted to the study of the critical group of a graph that is a cone over a generalized -graph.The main result of the article is an analog of the Plans theorem (1953), which describes the first homology group of an -sheeted cyclic cover of the three-dimensional sphere branched over a knot.It asserts that this homology group is almost a direct sum of two copies of a certain abelian group.In this paper, analogous results are established for the structure of the critical group of the graphs under consideration.
AB - We consider a family of graphs generalizing the family of -graphs, which in turn includes generalized Petersen graphs and prismatic graphs.The paper is devoted to the study of the critical group of a graph that is a cone over a generalized -graph.The main result of the article is an analog of the Plans theorem (1953), which describes the first homology group of an -sheeted cyclic cover of the three-dimensional sphere branched over a knot.It asserts that this homology group is almost a direct sum of two copies of a certain abelian group.In this paper, analogous results are established for the structure of the critical group of the graphs under consideration.
KW - 517.545+519.173+519.177
KW - Laplacian matrix
KW - Plans theorem
KW - circulant graph
KW - critical group
UR - https://www.scopus.com/pages/publications/105028605153
UR - https://www.mendeley.com/catalogue/503e9255-0353-33ca-8816-dd1516867c4b/
U2 - 10.1134/S0037446626010106
DO - 10.1134/S0037446626010106
M3 - Article
VL - 67
SP - 99
EP - 109
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
SN - 0037-4466
IS - 1
ER -
ID: 74322894